I think the lenses you buy must be determined by the type of photography you’re most interested in. If you like landscapes, then you’ll want to buy a wide angle lens. If you like portraits, then a short telephoto with a large maximum aperture is where you want to be. Shooting skittish animals requires a long telephoto.
It sounds like you’re interested in flexibility and “street scene” photography for the most part, because you’re talking about replacing the 18-55, what I call the “walk-around” range. You might consider upgrading to the 18-55 IS and save some money if you like that range;I understand many of the image issues with the non-IS version have been worked out with this model, plus it includes image stabilization. The 70-300 (which is not an L, by the way) doesn’t really replace your 18-55…I’d recommend that you hang on to the 18-55 if you buy this lens.
It is true that L glass is the best, but I don’t recommend it for beginning photographers. It’s expensive, and heavy, and if you’re not going to adapt your shooting style to make the best use of this higher quality glass, then it’s a lot of wasted money. I think that you should learn how to shoot in a way where the equipment is the limiting factor before you upgrade;that’s the path to managing your budget effectively. :-)
I would also recommend staying away from the “all-in-one” lenses with high focal length ratios, such as the 11x lens you describe. Those lenses are not very good for learning photography and tend to encourage lazy framing and composition habits, which is fine if you’re experienced and know when you can get away with it. Also, these lenses typically have small apertures, particularly at the long end, meaning you can’t shoot in lower light situations without a tripod. Often, the best pictures are made in lower light, while the sun is setting or rising and the oblique angle of the light can be used to show the texture and quality of your subject. (All in one lenses are very limiting indoors as well for the same reason…even indoor areas that seem fairly bright are many stops dimmer than outside on a sunny day.)
In general, Canon tends to make lenses of higher quality than third-party manufacturers, but this is not true for every model, so I’d encourage you to research the specific lenses and read reviews on third-party models you’re considering (a great location for information is dpreview.com). You should always have at least one Canon lens, though (I recommend the cheapest one: 50mm f/1.8, a great lens for the money, particularly for beginning photographers). Should you have any problems with your camera and require service during the warranty period, Canon will only provide support if you can prove it’s an issue with the camera and not the lens. (Sometimes lenses can fritz out and send wrong information, causing the camera to behave strangely.)